"Squaring the circle"
By J.J. O'Connor and E.F. Robertson (April 1999)
"There are three classical problems in Greek mathematics which were extremely influential in the development of geometry. These problems were those of squaring the circle, doubling the cube and trisecting an angle. Although these are closely linked, we choose to examine them in separate articles. The present article studies what has become the most famous for these problems, namely the problem of squaring the circle or the quadrature of the circle as it is sometimes called.
One of the fascinations of this problem is that it has been of interest throughout the whole of the history of mathematics. From the oldest mathematical documents known up to the mathematics of today the problem and related problems concerning π have interested both professional mathematicians and amateur mathematicians.
One of the oldest surviving mathematical writings is the Rhind papyrus, named after the Scottish Egyptologist A Henry Rhind who purchased it in Luxor in 1858. It is a scroll about 6 metres long and 1/3 of a metre wide and was written around 1650 BC by the scribe Ahmes who copied a document which is 200 years older. This gives date for the original papyrus of about 1850 BC but some experts believe that the Rhind papyrus is based on a work going back to 3400 BC.
In the Rhind papyrus Ahmes gives a rule to construct a square of area nearly equal to that of a circle. The rule is to cut 1/9 off the circle's diameter and to construct a square on the remainder. Although this is not really a geometrical construction as such it does show that the problem of constructing a square of area equal to that of a circle goes back to the beginnings of mathematics. This is quite a good approximation, corresponding to a value of 3.1605, rather than 3.14159, for π..."
Full Essay:
http://www-history.mcs.st-andrews.ac.uk/HistTopics/Squaring_the_circle.html
[Endnote from Rev. P.M. Lorca:
Within the Realm of Sacred Geometry, there are a number of practical uses for the squaring of a circle technique in conjure and bringing forth cosmic (universal) energies and transferences within the applied disciplines of Occult Metaphysics, "Specified" Occultism, and Ritual Magick practices, especially, in pyramidical energy work.]
